[blokeybloke]

Can we consider ions of elements to be elements? For example can we still call a potassium ion “potassium” or are its properties different to potassium? I often see that only atoms can retain properties of element.

[satirical_snowman]

Short Answer: Yes.

Long Answer: Ions of atoms have to do with electrons, you know, H⁺ has 0 electrons and H has 1 electron. While electrons play a significant role in how elements react, they don't play a major role in the properties of that element. The amount of protons, not electrons, is what affects the properties of the element.

So basically, for example, Cu⁺, Cu²⁺, and Cu are all labelled as Copper, even though the charge and reactivity might be different.

[mjc123]

The chemical properties of potassium ions are different from metallic potassium, but we don't consider it a separate element. It is "potassium in the ionic form" rather than "potassium in the metallic form". For example, someone once asked "if bananas contain a lot of potassium, why don't they catch fire in water?" The reason is that bananas contain ionic potassium, not metallic potassium. Potassium metal reacts strongly with water because formation of potassium ions is so favourable:
K(s) + H₂O  K⁺(aq) + OH^-(aq)
But once the potassium is in the ionic form, it shows no further reactivity towards water. You can put KCl (or bananas) in water without an explosion!